Heralded generation of high-purity ultrashort single photonsin arbitrary temporal shapes

Vahid Ansari1,∗ Emanuele Roccia2, Matteo Santandrea1, Mahnaz Doostdar

Kejdehi1, Christof Eigner1, Laura Padberg1, Ilaria Gianani2, Marco Sbroscia2,

John M. Donohue1, Luca Mancino2, Marco Barbieri2, and Christine Silberhorn1

1Integrated Quantum Optics, Paderborn University,Warburger Strasse 100, 33098 Paderborn, Germany and

2Dipartimento di Scienze, Universit‘a degli Studi Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy

We experimentally demonstrate a source of nearly pure single photons in arbitrary temporalshapes heralded from a parametric down-conversion (PDC) source at telecom wavelengths. Thetechnology is enabled by the tailored dispersion of in-house fabricated waveguides with shapedpump pulses to directly generate the PDC photons in on-demand temporal shapes. We generatePDC photons in Hermite-Gauss and frequency-binned modes and confirm a minimum purity of 0.81,even for complex temporal shapes.

I. INTRODUCTION

Preparing single photons in pure and controlledspectral-temporal modes is a key requirement for quan-tum photonic technologies. Diverse applications includ-ing quantum-enhanced metrology [1, 2], quantum com-putation [3, 4], and quantum encryption [5–7] rely onhigh-contrast interference through stable sources of puresingle photons. In addition, widely customisable and pre-cisely controllable temporal-mode shaping is necessary toensure mode matching between individual sources [8], fa-cilitate coupling between nodes in a quantum network [9],and enable temporal-mode based quantum communica-tion [10]. Furthermore, sources with high brightness areessential for scalable performance, and spatially single-mode behaviour is necessary for coupling to optical fibrenetworks and integrated waveguide devices.

Sources based on parametric downconversion (PDC)have granted a simple solution to heralded single-photongeneration for decades, but have not yet satisfied allof the above requirements simultaneously. Most PDCsources generate photons with strong spectral, corre-lations which is undesirable for heralded single-photonsources. However, it is possible to minimise the spectralcorrelation in crystals offering specific dispersion proper-ties along with an adapted pump bandwidth [8, 11–18].This specific dispersion property is linked to the groupvelocities of the pump and the PDC photons and can besummarised in two categories: matching the group ve-locity of the pump photon with one of the PDC photons[8, 17], or having the group velocity of the pump betweenthe two PDC photons [13–16].

On the other hand, efficient temporal-mode shaping ofthe PDC photons is more challenging. Existing methodsto create a broadband single photon in an arbitrary tem-poral mode rely on carving out the desired mode from theoriginal wavepacket as depicted in Fig. 1 (a), which can

∗ vahid.ansari@uni-paderborn.de

PUMPPUMP

HERALD

SIGNALSIGNAL

SHAPER

HERALD(a) (b)

FIG. 1. Heralded source of temporally shaped single-photons.(a) The desired temporal mode can be carved out of PDC pho-tons after the generation, which inevitably reduces the herald-ing efficiency. (b) With an appropriately designed pump fieldand group-velocity engineered nonlinear medium, the PDCphotons are emitted directly in a desired temporal shape. Inboth scenarios the purity of heralded single photon rely on theseparability of the PDC state in terms of signal and heraldfields.

be accurately achieved by temporal or spectral modula-tion of the photon [19–23]. This method, however, neces-sarily introduces loss and leads to a reduced rate of pre-pared photons [24] and a low pair-symmetric heraldingefficiencies [25]; this poses a practical limit for many ex-periments such as device-independent quantum cryptog-raphy [26, 27] and optical quantum computing [28–30].Temporal manipulation is also possible with shaped-pulsemediated nonlinear interactions [9, 31–34], Raman inter-faces [35], or ultrafast electro-optic modulation [36], butthese methods are experimentally challenging to imple-ment without prohibitive loss. To minimise the potentialfor photon loss, a source which generates heralded pho-tons in a customisable and pure spectral state is highlydesirable.

In this letter, we take a novel approach to directlycreate PDC photons with tailored temporal-modes.Through group-velocity matching two of the interactingfields in the PDC process, we generate heralded photonswhich inherit the temporal shape of the pump pulse, assketched in Fig. 1 (b). We show through joint spectralmeasurements and second-order photon number correla-tions that the photons are generated in a highly purestate. We explicitly demonstrate the versatility of oursource design by generating photons with customised

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temporal shapes, such as broadband Hermite-Gaussiantemporal modes and narrow frequency bins. Our sourceis based on the in-house fabricated unpoled KTP waveg-uides and emits in the near-infrared telecommunicationsregime, making it a prime candidate for use in long-distance quantum protocols and fibre-based networks.Our result bridges an important gap in quantum stateengineering of time-frequency modes, and enables a rangeof quantum photonic applications that require temporal-mode matching.

II. THEORY

The PDC process in the waveguides happens when theenergy conservation ωp = ωs+ωi and the momentum con-servation kp = ks + ki between the three fields — pump,signal, and idler — are satisfied. The momentum conser-vation with waveguided collinear propagation is typicallyachieved with quasi-phasematching through periodic pol-ing. In our case, we consider a type-II PDC processwhere momentum conservation is enabled by birefringentphasematching without a need for periodic poling. Thewaveguided structure we consider is made with a z-cutKTP substrate and waveguides fabricated along the x-axis of the crystal with rubidium ion exchange. To cal-culate the effective refractive indices of the optical fieldsinside of the Rb:KTP waveguide, we use a commercialfinite-element mode solver along with a model for therefractive index profile provided in [37]. Theoreticallycalculated phasematched type-II processes for differentpump wavelengths are plotted in Fig. 2 (a) as solid lines,where we also experimentally verified our model (see thecaption).

The Hamiltonian of type-II PDC process is

HPDC ∝∫∫

f(ωs, ωi)a†TM(ωs)a

†TE(ωi)dωsdωi + h.c., (1)

where a†(ω) is the standard creation operator at fre-quency ω. The joint spectral amplitude (JSA) function

f(ωs, ωi) = α(ωs + ωi)φ(ωs, ωi), (2)

describes the spectral-temporal properties of the PDCstate, where α(ωs, ωi) is the ultrashort pump amplitudefunction and φ(ωs, ωi) is the phasematching function ex-pressing the momentum conservation between the fieldsin the waveguide. Due to energy conservation, PDCsources typically exhibit spectral correlations. However,many applications benefit from spectrally pure single-photon states with separable JSAs of the form

f(ωs, ωi) ≈ g(ωs)h(ωi), (3)

which can be achieved by dispersion engineering.The strength of spectral correlations in the PDC state

can be quantified by a Schmidt decomposition of theJSA function[38, 39]. This defines the Schmidt num-ber K as the effective number of temporal-modes in the

(a) (b)

FIG. 2. (a) Birefringent phasematched type-II PDC processesin the KTP waveguide versus pump wavelength. The pumpand idler photons are TE polarised and the signal photon isTM polarised. The dots correspond to experimentally mea-sured PDC photons with a tunable pulsed pump laser anda single-photon sensitive spectrometer. The data point atthe degeneracy point, however, is measured by means of sec-ond harmonic generation with a pulsed pump at the centralwavelength of 1275 nm. The error bars are smaller than themarkers. (b) Spectral purity of the JSA for different pumpbandwidths ∆λp and crystal lengths L.

state. An experimentally accessible method to measurethe Schmidt number and the purity P of the PDC pho-tons is by means of second-order correlation functiong(2)(τ = 0) of unheralded signal or idler photons as [40]

P =1

K= g(2)(0)− 1. (4)

In the case of spectrally pure PDC state with K = 1, thepartial trace of the PDC state exhibits thermal photonnumber statistics corresponding to g(2)(0) = 2. Witha multimode state, we would measure a convolution ofall the different thermal photon statistics, since the de-tector cannot discriminate each mode, which results ina Poissonian photon-number distribution and a g(2)(0)that approaches 1 [41].

To realise a single-mode JSA we exploit a phasematch-ing with matched group-velocities of pump and signalfields, known as the asymmetric group-velocity match-ing (AGVM) condition [42]. This condition holds for apump wavelength of 670 nm (TE polarised) and a signalwavelength of 1411 nm (TM polarised), which are markedwith stars in Fig. 2 (a). In order to find the experimentalsettings for an optimum spectral purity, we calculate Pfor different pump pulse bandwidths and crystal lengthsas plotted in Fig. 2 (b). In our experimental implemen-tation, we use the AGVM condition with a pump spectralFWHM of 2 nm and a crystal length of 16 mm. This con-figuration leads to a nearly single-mode JSA as plotted inFig. 3, where we plot the JSA function with the pump inthe first-order Hermite-Gauss mode. From the JSA andits marginal distributions in Fig. 3 (c), it is clear thatthe phasematching function is mapped onto the idler pho-ton, while the spectral profile of the pump is impartedinto the signal photon. A similar AGVM condition canbe also achieved in a periodically poled bulk KTP but at

3

(a) (b) (c)

FIG. 3. (a) The absolute value of the pump spectrum|α(ωs, ωi)| with the first-order Hermite-Gaussian profile withFWHM of 2 nm. (b) Phasematching function |φ(ωs, ωi)| ofa KTP waveguide with a length of 16 mm. (c) Theoreticaljoint spectral amplitude |f(ωs, ωi)| of the PDC state and itsmarginal distributions. The modelled JSA shows a Schmidtnumber of K = 1.087 and a spectral purity of P = 0.919.

wavelengths outside of the telecom bands [17]. Addition-ally, the waveguided structure, in comparison to bulk,accommodates a longer interaction length and a strongerfield confinement, allowing for higher parametric gainsand narrower phasematching functions. Note that a nar-row phasematching is crucial for high fidelity shaping ofthe signal photon.

III. EXPERIMENT

The outline of the experimental setup is given in Fig.4. To prepare the pump of the PDC process, we takeultrashort pulses at the central wavelength of 670 nm(from a frequency doubled optical parametric oscillator)and use a pulse shaper to carve out the desired temporalmodes. The pulse shaper is a folded 4f-setup consist ofa magnifying telescope, a holographic diffraction gratingwith 2000 lines per mm, a cylindrical silver mirror and atwo-dimensional reflective liquid crystal on silicon spatiallight modulator [43, 44]. This 4f-setup has a spectral res-olution of 35 pm which along with the initial 6 nm band-width of our laser system allows us to accurately preparee.g. Hermite-Gaussian pulses of up to fourth order with2 nm of FWHM for the Gaussian profile. We use spec-tral interferometry to characterise the performance of thepulse shaper and ensure a dispersion-free alignment [45].

The heart of the experiment is a 16 mm long in-housebuilt Rb:KTP waveguide with a nominal width of 3 µmand depth of 5µm and is designed to be spatially single-mode over the whole telecom range for both TE andTM polarisations. Using the FabryPerot interferomet-ric method [46] we measure internal waveguide losses of0.85 dB/cm and 0.67 dB/cm at 1550 nm for TE and TMpolarisations, respectively. To estimate the maximumachievable coupling efficiency of the waveguide mode intothe standard single-mode telecom fibre (SMF-28) we usebright lasers matched with central frequencies of the PDCphotons and measure coupling efficiencies of 0.65 and0.60 for idler (TM) and signal (TE) photons, respectively.This is due to asymmetry of the waveguide mode which

PUMP

Rb:KTPWAVEGUIDE

SMF

PBS

4FSETUP

4FSETUP

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SIGNAL1276nm

IDLER1411nm

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OPOSHG

1340nm

Phasematching function

FIG. 4. Experimental setup. To prepare ultrashort pumppulses at 670 nm we take second harmonics (SHG) of an op-tical parametric oscillator (OPO). For the spectral shapingwe use a spatial light modulator in a 4f-setup to shape thespectral amplitude and phase of the pump field. The gener-ated PDC photons are then separated on a broadband po-larising beamsplitter (PBS). We use 4f-setups for both PDCphotons to filter the undesirable background. Finally eachbeam is coupled into single-mode fibres (SMF) for telecomwavelengths. The plot compares the theoretical and experi-mentally measured phasematching functions.

can be designed to be more symmetric at any chosenwavelength by modifying the fabrication parameters e.g.the diffusion depth. The waveguide used in this workhas a more symmetric mode profile at 1550 nm where wemeasure a coupling efficiency of more than 0.80.

To spectrally filter the pump field and the parasiticbackground noise, we use folded 4f-setups in each arm,aligned around the central frequencies of PDC photons.The total transmissions of 4f-setups are 0.26 and 0.30for signal and idler photons, respectively, owing prin-cipally to a low diffraction efficiency of the diffractiongratings. The PDC photons are then detected with fibrecoupled superconducting nanowire single photon detec-tors (SNSPD) with system detection efficiencies of 0.41and 0.55 at 1276 nm and 1411 nm, respectively. Withthis configuration we measure Klyshko efficiencies of 8%and 5% for signal and idler photons, respectively. A nor-malisation over the transmission of 4f-setups (which canbe replaced with bandpass filters with very high trans-missivities) and detection efficiencies, these Klyshko effi-ciencies can be improved to 56% and 40% for signal andidler photons, respectively.

III.1. Spectral characterisation

To measure the spectrum of the idler photon, we usethe 4f-setup in the monochromator configuration, witha spectral resolution of 0.2 nm. With the AGVM con-

4

(a)

(e)

(d)

(c)

(b)

FIG. 5. A few examples of the measured joint spectral inten-sities (JSIs), with the marginal spectral distribution of sig-nal photon above in grey. The pump mode for each JSI isshown on the right side, where the grey shaded area is thespectral amplitude and the green line is the spectral phase.The pump modes are as the following: (a) Gaussian, (b) 1st-order Hermite-Gaussian, (c) 2nd-order Hermite-Gaussian, (d)3rd-order Hermite-Gaussian, (e) frequency bins, with Schmidtnumbers: Ka = 1.01, Kb = 1.01, Kc = 1.02, Kd = 1.02,Ke = 1.02.

dition, as can be seen in Fig. 3 (right), the spectrumof the idler photon echoes the phasematching functionφ(ωs, ωi). The measured spectrum of the idler photonand its theoretical counterpart are plotted in Fig. 4.The discrepancy between experiment and theory can beexplained by considering the waveguide inhomogeneities[47–50]. An inhomogeneity of the waveguide channel,e.g. non-uniform width or depth, can change the effec-tive refractive index along the propagation direction andconsequently distort the phasematching function. Thebroadened phasematching with asymmetric side-lobes di-minishes the spectral purity and the fidelity of single pho-ton shaping, hence we use spectral filtering on the idlerphotons to remove the side-lobes. The filtering increasesthe purity at the cost of heralding efficiency.

To measure joint spectral intensity (JSI) distribution|f(ωs, ωi)|2, we combine the monochromator in the idlerarm with a time-of-flight spectrometer in the signal arm[51]. In the time-of-flight spectrometer we use a highlydispersive fibre to map the spectrum into the temporalprofile which can be resolved directly in time on SNSPDs.We use a fibre with a total dispersion of 0.3 ns/nm whichalongside with 70 ps timing resolution of SNSPD consti-tute a spectrometer with a resolution of about 0.2 nm.The measured JSIs with the pump field in the first fourHermite-Gauss modes and five frequency bins are plottedin Fig. 5. The Schmidt number inferred from these JSIs

(a) (b)

FIG. 6. The second-order correlation measurements of theidler and signal photons with the pump set to different band-widths and different orders of Hermite-Gaussian modes. Theerror bars for the g

(2)signal(τ = 0) are smaller than the markers.

shows a spectral purity of more than 0.98, which providesan upper bound on the spectral purity.

III.2. Purity and second-order correlation function

As discussed in the theory section, spectral correlationsbetween PDC photons leads to impurity of the heraldedsingle photons. Although the JSI measurement provideimportant information about the spectral correlation ofthe PDC photons, it is blind to the spectral phase of thephotons and is also limited by the resolution of the spec-trometers. A better measure of any underlying correla-tions of the PDC photons is the second-order correlationfunction g(2)(0) of signal or idler photons, as measuredwith a 50/50 fibre coupler [40, 52]. The g(2)(0) measure-ment probes the photon number statistics of unheraldedbeams (signal or idler) and can discriminate between asingle-mode PDC state with g(2)(0) = 2 and a highlymultimode state with g(2)(0) = 1. In Fig. 6 we plot theg(2)(0) of the both PDC photons with the pump pulsein different orders of Hermite-Gauss modes and band-widths ranging from 0.5 nm to 3 nm. With a narrowpump bandwidth, energy correlations remain in the PDCstate which are exhibited in lower g(2)(0) values. For theidler photon, we spectrally filter the asymmetric phase-matching side-lobes (see Fig. 4), and we achieve the high-est g(2)(0) of 1.99 ± 0.02 with a 1.5 nm broad Gaussianpump pulse, which reduces to 1.93±0.02, 1.85±0.02, and1.81±0.02 for the first, second, and third order Hermite-Gauss modes, respectively. The corresponding puritiescan be calculated through Eq. 4.

The g(2)(0) of signal photons, plotted in Fig. 6 (b),is considerably lower. This is due to the presence of thephasematching side-lobes which cannot be simply filteredfor the signal photons (see Fig. 3 (c)). While the signalphotons are themselves less pure, the high g(2)(0) of theidler indicates that the shaped signal photons are highlypure when heralded by an idler detection. This puritythus comes at a cost of heralding efficiency. Enhancingthe waveguide fabrication technology or using methods

5

such as noncritical phasematching [53] or aperiodic pol-ing [54, 55] may be able to eliminate these unwantedspectral features to produce filter-free heralded photonswith high purity and arbitrary temporal shape.

III.3. Conclusion

We have shown that heralded single photons can begenerated in arbitrary temporal modes using pulse shap-ing and KTP waveguides with an optimised dispersion.Through joint spectral intensity measurements, we haveverified that the spectral shape of the pump pulse isfaithfully imparted onto the signal photon. Second-order photon number correlations measurements showthat the heralded photon state is highly pure and suit-able for use in quantum networks. Our integrated sourceis based on birefringent phasematching and emits withinthe telecommunications band. Future work will focus onadapting the source with periodic poling to optimise theemission wavelengths for available photon detectors and

customise the joint spectral amplitude to eliminate theneed for filtering. With these optimisations, the sourcepresented here will prove to be a vital component in ap-plications such as temporal-mode based quantum com-munication and mode matching between quantum inter-faces.

ACKNOWLEDGEMENTS

E.R. thanks the integrated quantum optics group fortheir hospitality during the completion of this work. Wethank Fabio Sciarrino for fruitful discussion.

FUNDING INFORMATION

This research has received funding from the GottfriedWilhelm Leibniz-Preis and from the European UnionsHorizon 2020 research and innovation programme undergrant agreement No 665148.

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